# Chapter 2 - Limits - 2.6 Trigonometric Limits - Exercises - Page 77: 24

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#### Work Step by Step

\begin{align*} \lim _{\theta\rightarrow 0} \frac{ 1 -\cos \theta }{\sin\theta } &=\lim _{\theta\rightarrow 0} \frac{ 1 -\cos \theta }{\sin\theta } \frac{\theta}{\theta}\\ &= \lim _{\theta\rightarrow 0} \frac{ 1- \cos \theta }{\theta } \lim _{\theta\rightarrow 0} \frac{\theta}{\sin \theta}\\ &=0. \end{align*} Where we used the facts that $\lim _{\theta\rightarrow 0} \frac{ 1- \cos \theta }{\theta } =0$ and $\lim _{\theta\rightarrow 0} \frac{ \theta }{\sin \theta } =0$

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